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Math Help - Probability problem

  1. #1
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    Probability problem

    I would appreciate if you can solve this. Thank you.


    A radio station in central Pennsylvania is having a birthday contest. One of the 366 days of the year is randomly selected with equal probability. If the month of a contestant's birthday matches the month selected - or the day of the month of the contestant's birthday matches the day of the month selected - or both - the contestant wins a compact disc. Otherwise, the contestant wins nothing. What is the probability that a contestant with a December 31 birthday will win? Express your answer as a common fraction.
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  2. #2
    MHF Contributor
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    Hi chil2e,

    In a 366-day year, if each day is equally likely of being selected,

    then the probability of a December day being selected is \frac{31}{366}.

    The probability of the daydate 31 being selected is \frac{7}{366}.

    If we sum the probabilities and subtract the overlapping day, Dec 31,
    due to double-counting, we will have the probability that a contestant
    with a Dec 31 birthday will win.

    This is \frac{31}{366}+\frac{7}{366}-\frac{1}{366}
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